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SYSTEMATIC DESIGN AND ANALYSIS OF STEP RATE TESTS TO 4 DETERMINE FORMATION PARTING PRESSURE. SPE 16798 long enough to overcome wellbore storage and achieve Fig. 8 is a Log Ap vs. tog W plot for Case 1. radial flow. For a radial system, equations are Data for the storage dominated first three steps lie available in the liter©turel� 12 to calculate the on a unit slope Line. The rapid increase in pres- time when wellbore storage effects become negli- sure during step 4 is caused by changing (reduced) gibLe. If the time step size thus calculated is too wellbore storage. The p vs. q plots for Case 1 large, smaller time steps may have to be used for and 2 are compared on Fig. 9. The pretest pressure practical considerations. The analysis of such a (1000 psi) and end points for steps 1, 2 and 3 have Lest, however, will be affected by weLLbore storage, a concave upward curvature. This feature is further andif fillup occurs, by changing wellbore enhanced by including the effect of changing storage storage.4 This is especially true for some pressure during step 4. The true preparting straight line, depleted reservoirs where reservoir pressure is formed by end points for steps 4, 5 and 6, for Lower than the hydrostatic pressure. Case 1, extrapolates back close to the pretest pres- sure point. A straight Line through points above 2. Wellbore Storage the parting pressure (steps 5 and 6, Case 2), how- ever, intersects the y-axis at a pressure much above Three SRTs were simulated to investigate the the pretest pressure. It should be emphasized that applicability of multirate analysis to SRT data it would be incorrect to force fit a straight line influenced by wellbore storage. For each case, time through storage and/or changing storage dominated steps were so chosen that steps end in a (i) purely steps and interpret the intersection of this and a radial, (ii) storage-radial transition, and true preparting straight line (if one exists) as (iii) entirely storage dominated flow regime, parting pressure. respectively. For each case, Log-log plots of Agar- wal's multirate equivalent times are presented in FelsenthaL2 attributes the concave upward cur- Figs. 5, 6 and 7, respectively. Multirate superpo- vature for the early steps on the p vs. q plot to sition is applicable for the radial flow regime non-D'Arcy flow downstream from the pressure meas- case, as expected (Fig. 5). Surprisingly, superpo- uring device. While this is certainly a possi- sition method also appears to work for the storage- bility, wellbore storage and, if wellbore fiLlup radial transition flow regime case (Fig. 6). The occurs, changing storage have the same effect on the true semi-log straight Line is, however, not devel- p vs. q plot. Generally, considering the lower oped for an accurate kh analysis. Applicability of injection rates for the early steps of a SRT, well- multirate analysis breaks down for the storage domi- bore storage seems to be a more likely explanation nated case (Fig. 7). This suggests that time step for this behavior. size should be tong enough for the data to be at Least in a storage-radial transition period. Figs. 10 and 11 are the Odeh and Jones multi- rate plots for Case 1 and 2, respectively. Even To identify if SRT pressure data are completely though radial flow superposition is not rigorously dominated by wellbore storage effects, a new plot is applicable during the storage dominated first three suggested. Applying multiple rate superposition to steps, the following comments are in order for the the storage dominated flow Eq. (5):4 general characteristics of the plots: (i) the rapid increase in pressure caused by changing wellbore storage is reflected as a much steeper plot of data pi - pwf - 24C .......... ...(5) points for the fourth step, (ii) data for the fifth and sixth steps fall together for the no fracture extension case shown in Fig. 10, when storage has for the case of multiple rate injection, will yield been reduced and the effect of pressure response caused by changing storage has diminished. For the fracture extension case shown in Fig. 11, a downward _ __ 8 shift in data is noted for each successive step pwf pi 24C �W� """""".(6) above the parting pressure (steps 5 and 6). Note that it is possible to reach the parting where W = cumulative injection pressure at the same time that the wellbore com- pletely fills up. This phenomenon was simulated by Eq. 6 suggests that a plot of log (p f - p.) initiating fracture extension (i) at the beginning versus log (W) will yield a line of unit slope �or of step 4, and (ii) during step 4. Results were data completely dominated by a constant weLLbore very similar to Fig. 11. In this situation, the storage. This is verified in the next section. exact parting pressure was found to be masked by the changing wellbore storage pressure response. How- 3. Changing Wellbore Storage ever, it was possible to distinguish whether the data following this step were above or below the Six-step SRTs were simulated to investigate the parting pressure. effect of changing wellbore storage from a rising fluid level type (high) to a compressive (low) type. 4. Rate Increment In each case, C was reduced from 105, for the storage dominated first three steps, to 103 for the FelsenthaL2 suggested using rates of 5, 10, 20, last three steps. Two cases are compared here: 40, 60, 80 and 100 percent of the anticipated max- i) Case 1 - no fracture for the entire SRT simula- imum test rate as a possible rule of thumb. ALL the Lion, and (ii) Case 2 - a fracture of 2.5 Et half- simulated SRTs presented in this paper use equal length introduced at the beginning of step 5 and rate increments. The theoretical basis for the p subsequently increased to 5.0 Et at the beginning of vs. q plot or multirate analysis, however, does not step 6. Case 2 is intended to simulate fracture extension following changing weLLbore storage. 494